Centre for Mathematical
Sciences
Wilberforce Road, Cambridge, CB3 0WB
Tel: (01223) 337958
Fax: (01223) 337956
Email: secretary@statslab.cam.ac.uk
All interested are welcome
This list is subject to revision
Select a date to view the relevant seminar abstracts:
We review Terry Lyons' theory of "rough paths" and discuss its applications to Brownian motion. The Stroock-Varadhan support theorem is obtained as corollary.
We describe a nice example of duality between coagulation and fragmentation associated with certain Dirichlet distributions. The fragmentation and coalescence chains we derive arise naturally in the context of the genealogy of Yule processes.
The goal of the talk is to review the various ways of addressing the volatility smile issue, from "local volatility" and stochastic volatility models to jump processes. A particular attention will be dedicated to pure jump Lévy processes, with the possible addition of stochastic volatility: calibration of the volatility surface will be discussed in this setting. Lastly, some mathematical elements on "local Lévy" models will be presented.
Consider a queueing system of two servers and three arrival flows. Flows 1 and 2, of loads $\rho_1$ and $\rho_2$, are dedicated and always go in the buffers of servers 1 and 2, respectively. Tasks from flow 0 join the queue which has the smaller workload at the time of arrival. The subcriticality condition is that $\rho_i<1$, > $i=1,2$, and $\rho_0+\rho_1+\rho_2<2$. The talk studies Large deviations in the stationary regime for the virtual waiting time in the opportunistic flow $\rho_0$.When the arrival flows are M/GI, with non-heavy service-distribution tails, the system can be analysed in a straighforward fashion: the answer depends on a balance condition $\rho_0>|\rho_1-\rho_2|$. However, it is interesting (and challenging) to discuss a general case of flows with heavy tails and/or dependencies. The talk will focus on an ongoing work (by K. Duffy, D. Malone, E. Pechersky, Y. Suhov and N. Vvedenskaya) where Large deviation predictions are numerically checked for a variety of arrival flows.
In this talk, we analyse implied volatility models defined by assuming that the per-delta short-dated smile is stochastic. We derive the differential equation satisfied by the short-dated smile that ensures no-arbitrage. We solve this equation in particular cases and we obtain analytical expressions for the corresponding short-dated smile that generalises the formulae derived by P. Hagan when the volatility is lognormal and correlated with spot.